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Approximate solution to abstract differential equations with variable domain

Year: 2010

Type: preprint

Abstract: A new exponentially convergent algorithm is proposed for an abstract the first order differential equation with unbounded operator coefficient possessing a variable domain. The algorithm is based on a generalization of the Duhamel integral for vector-valued functions. This technique translates the initial problem to a system of integral equations. Then the system is approximated with exponential accuracy. The theoretical results are illustrated by examples associated with the heat transfer boundary value problems.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1003.2537

Authors: Bohonova, T. Ju., Gavrilyuk, I. P., Makarov, V. L., Vasylyk, V.

Institutions: National University "Kyiv Aviation Institute", Institute of Mathematics

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Deutsche Forschungsgemeinschaft

OpenAlex ID: W1724255874

Cites: 7

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Related to: 10